Q$-2$ A countershaft is supported by two tapered roller bearings using an indirect mounting. The radial bearing loads are $2\mathrm{.}5$ kN for the left$-$hand bearing and $4\mathrm{.}9$ kN for the right$-$hand bearing. An axial load of $0\mathrm{.}9$ kN is carried by the left bearing. The shaft rotates at $\backslash (880\backslash$mathrm$\{$rev$\}/\backslash$mathrm$\{$min$\}\backslash )$ and is to have a desired life of $16$ kh $.$ Use an application factor of $1\mathrm{.}3$ and a combined reliability goal of $0\mathrm{.}99.$

$($a$)$ Give a proper drawing indicating the suggested indirect mounting and using an initial $\backslash ($ K$\_\{$A$\}\backslash )\backslash (=$K$\_\{$B$\}=1\mathrm{.}5\backslash ),$ find the required radial rating for each bearing. Select the bearings from the Timken Catalog pages given in Fig. $11-15($Shigley$).$

$($b$)$ Determine the resulting overall reliability for the assigned bearing set. $[15$ pts$.]$